Conventional air-conditioning units may include an evaporator producing cool air, a heater producing hot air, a bypass path allowing the cool air to bypass the heater, an air-mixing door adjusting an air-flow ratio between an amount of cool air passing through the heater and an amount of cool air passing through the bypass path, an air-mixing chamber in which the air from the heater and the air from the bypass path are mixed, and at least one air opening from which the mixed air may be discharged. In the conventional air-conditioning units, as the air-mixing door opens the bypass path slightly from a maximum heating position, in which the air-mixing door may fully close the bypass path, a significant amount of cool air may rapidly flow through the narrow bypass path. As a result, the temperature of the mixed air discharged from the air opening may decrease sharply as shown by the chain double-dashed line in FIG. 5, which illustrates a temperature characteristic of mixed air with respect to a position of the air-mixing device for a conventional air-conditioning unit (chain double-dashed line), an embodiment of the present invention (solid line), and an ideal case (dashed line).